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Chapter-wise /Concepts for One-Mark Questions (Samacheer Kalvi 12th Maths):
Volume 1
Chapter 1:
Applications of Matrices and Determinants
- Matrices: Order of a matrix, Types of
matrices (square, rectangular, identity, zero, diagonal, scalar,
upper/lower triangular, symmetric, skew-symmetric), Transpose of a matrix,
Adjoint of a matrix, Inverse of a matrix.
- Determinants: Determinant of a matrix,
Properties of determinants, Singular and Non-singular matrices.
- Applications: Rank of a matrix (minor
method, row reduction method, echelon form), Consistency of system of
linear equations (Cramer's Rule, Matrix Inversion Method, Gaussian
Elimination method), Elementary transformations.
- Key terms: Adjoint, inverse, rank,
consistency, trivial solution, non-trivial solution.
Chapter 2:
Complex Numbers
- Complex Numbers: Definition of a complex number
(z=x+iy), Real part (Re(z)), Imaginary part (Im(z)), Conjugate of a
complex number (zˉ).
- Algebra of Complex Numbers: Addition, subtraction,
multiplication, division of complex numbers.
- Modulus and Argument: Modulus (∣z∣), Argument (arg(z)), Principal
Argument.
- Forms of Complex Numbers: Cartesian form, Polar form,
Euler form (eiθ=cosθ+isinθ).
- De Moivre's Theorem: Its applications for finding
powers and roots of complex numbers.
- Geometric Interpretation: Locus of complex numbers,
properties related to circles, lines in the complex plane.
- Roots of Unity: Cube roots of unity, nth roots
of unity and their properties.
Chapter 3:
Theory of Equations
- Polynomial Equations: Degree of a polynomial, Roots
of an equation.
- Fundamental Theorem of Algebra: Every polynomial equation of
degree n has exactly n roots (counting multiplicity).
- Formation of Polynomial
Equations:
From given roots.
- Relationship between Roots and
Coefficients:
Vieta's formulas for quadratic, cubic, and quartic equations.
- Nature of Roots: Real, imaginary, rational,
irrational roots.
- Reciprocal Equations: Definition and methods of
solving.
- Transformation of Equations: Transforming an equation into
another with roots scaled, reciprocated, or changed in sign.
Chapter 4:
Inverse Trigonometric Functions
- Inverse Trigonometric
Functions:
Domain and Range, Principal Value Branch.
- Properties of Inverse
Trigonometric Functions: Identities involving sin−1x, cos−1x, tan−1x, etc.
- Graphs of Inverse Trigonometric
Functions.
- Conversions: Converting one inverse
trigonometric function into another.
Chapter 5:
Two Dimensional Analytical Geometry - II
- Conics: Definition of conic section,
Focus, Directrix, Eccentricity (e).
- Parabola: Equation of parabola, Vertex,
Focus, Directrix, Latus Rectum, Standard forms.
- Ellipse: Equation of ellipse, Center,
Foci, Vertices, Major and Minor axes, Eccentricity, Latus Rectum, Standard
forms.
- Hyperbola: Equation of hyperbola, Center,
Foci, Vertices, Transverse and Conjugate axes, Eccentricity, Latus Rectum,
Asymptotes, Standard forms.
- Parametric Equations of Conics.
- Tangent and Normal to Conics.
Chapter 6:
Applications of Vector Algebra
- Vectors: Position vector, Direction
cosines and ratios, Scalar product (dot product), Vector product (cross
product).
- Scalar Triple Product: Geometric interpretation
(volume of parallelepiped), properties.
- Vector Triple Product.
- Applications: Area of
triangle/parallelogram, Volume of parallelepiped/tetrahedron.
- Lines in 3D: Vector and Cartesian equations
of a line (passing through a point and parallel to a vector, passing
through two points).
- Planes in 3D: Vector and Cartesian equations
of a plane (normal form, passing through a point and normal to a vector,
intercept form, passing through three non-collinear points, passing through
a point and parallel to two vectors).
- Angle between: Two lines, two planes, a line
and a plane.
- Distance between: Two points, a point and a
line, two parallel lines, two skew lines, a point and a plane.
ONE MARKS
12th Maths EM Book Back One Mark Online Quiz : Download Here
12th Maths TM Book Back One Mark/ Prepared By: V.Gnanamurugan, PGT, GHSS, O.Siruvayal, Sivagangai Dt Pdf Link : Download Here
12th Maths EM Book Back One Mark / Prepared By: V.Gnanamurugan, PGT, GHSS, O.Siruvayal, Sivagangai Dt Pdf Link : Download Here
12th Maths EM Book Back One Mark/ Prepared By: M.Karthigai Gnapathy M.Sc., M.Ed., Pdf Link : Download Here
CREATIVE ONE MARKS
12th Maths Vol - 1 & 2 Creative 1m Question pdf link : Download Here
12th Maths Vol - 2 Creative 1m Question & Answer pdf link : Download Here
12th Maths EM Vol 2 Creative One Mark Solved Answer Video : Download Here
12th Maths EM Vol 1&2 Creative Question Prepared By: Nithish's Maths Pdf Link : Download Here
Volume 2
Chapter 7: Applications of Differential Calculus
- Derivatives: Concepts of continuity and differentiability.
- Tangent and Normal: Equation of tangent and normal to a curve.
- Monotonicity: Increasing and decreasing functions.
- Extrema: Local maxima and minima (first and second derivative tests).
- Concavity and Convexity: Points of inflection.
- Mean Value Theorems: Rolle's Theorem, Lagrange's Mean Value Theorem.
- L'Hopital's Rule: Evaluation of indeterminate forms.
- Related Rates.
- Approximation using Differentials.
Chapter 8: Differentials and Partial Derivatives
- Partial Derivatives: First order and second order partial derivatives.
- Euler's Theorem for Homogeneous Functions: Verification and application.
- Total Differential.
- Approximation and Errors using Differentials.
Chapter 9: Applications of Integration
- Definite Integrals: Properties of definite integrals.
- Area Under Curves: Area bounded by simple curves, area between two curves.
- Volume of Revolution: Volume of solids obtained by revolving an area about an axis.
- Gamma Integral.
- Reduction Formulae.
- Bernoulli's Formula for Integration by Parts.
Chapter 10: Ordinary Differential Equations
- Differential Equations: Order and Degree of a differential equation.
- Formation of Differential Equations.
- Methods of Solving Differential Equations:
- Variable separable method.
- Homogeneous differential equations.
- Linear differential equations.
- Exact differential equations (introduction).
- Applications: Growth and decay models, Newton's law of cooling.
Chapter 11: Probability Distributions
- Random Variables: Discrete and continuous random variables.
- Probability Mass Function (PMF): For discrete random variables.
- Probability Density Function (PDF): For continuous random variables.
- Cumulative Distribution Function (CDF).
- Mean and Variance of Random Variables: Expected value.
- Binomial Distribution: Properties, mean, variance.
- Poisson Distribution: Properties, mean, variance.
- Normal Distribution: Properties, standard normal distribution.
Chapter 12: Discrete Mathematics
- Mathematical Logic: Statements, Logical connectives (AND, OR, NOT, Implication, Bi-implication), Truth tables, Tautology, Contradiction, Contingency.
- Quantifiers: Universal quantifier (∀), Existential quantifier (∃).
- Boolean Algebra: Basic postulates, Boolean functions, Switching circuits (AND gate, OR gate, NOT gate).
- Groups: Binary operation, Properties of a group (closure, associative, identity, inverse), Abelian group.
- Subgroups.
- Finite and Infinite Groups.
ஆசிரியர்கள் தங்கள் மாணவர்களுக்கு தயார்செய்யும் படைப்புகளை 9003450850 என்ற எண்ணிற்கு அல்லது kanimathsedu@gmail.com மின்னஞ்சலுக்கு அனுப்பி வைக்கலாம். தங்கள் படைப்புகள் உலகறிய மாணவர்களுக்கும் பயன்படும். மேலும் தங்கள் பெயர் படிப்புகள் நமது www.kanimaths.com website பதிவேற்றம் செய்யப்படும்.
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